RFID is a technology for contactless cards. A basic smart card is not RFID-able; for decades, payment smart cards were not RFID; to talk to the chip you had to plug to it (that's what happens in a payment terminal).
In recent years, a number of banks have begun to promote some extra "electronic cash" systems. With such a system, an RFID-able chip is added into a credit card which may also have a non-RFID chip. The contactless transactions are kept separate from the "normal" transactions; possibly, the card contains two distinct chips which are physically separated; or maybe the separation is only "software". However, the rules for both kind of transactions are normally distinct, for three reasons:
- The contactless interface might conceivably be abused more easily since, by definition, it is contactless.
- The convenience of the contactless interface would be severely diminished if the user still had to type his PIN code. The contactless payment is meant for small, everyday transactions (e.g. when you buy a croissant in a bakery) which are supposed to be conducted as fast as possible.
- When using the contactless interface, the chip draws power from the variable magnetic field of the reader; this is much less power than what can be obtained through the normal connector. Correspondingly, the RFID chip is generally unable to perform extensive computations; in particular, digital signatures are out of the question.
So the expected result is that when a credit card has a chip AND can engage in contactless payment operations, then the latter is only about a small, finite "wallet" with at most 100$ in it or so; and completely hacking the card through its RFID interface does not give access to the main credit line of the card owner.
An extra source of confusion is that the concept of smart cards was patented in France in 1986. Many non-French banks, in particular in North America, thus decided not to deploy smart cards until the patent expired (in 2006). Before 2006, thus, these banks regularly justified their opposition to smart cards by sleazy suggestions about the "insecurity" of smart cards (these were damn lies, but they worked well with the customers). In 2006, right on cue, began to appear TV commercials about how banks had just discovered a new technology which is super-safe to protect card owners: the smart card. (Technically, this also is a damn lie; smart cards have never been about protecting customers; smart cards are about protecting banks because banks are ultimately responsible for transaction security, and are legally obliged to refund customers when fraud occurs.)